Many finite-dimensional minimization problems and nonlinear equations can be solved using Secant Methods. In this thesis, we present a historical development of the (n + 1)-point Secant Method tracing its evolution back ...

The advent of parallel processing systems has resulted in the potential for increased performance over traditional uniprocessor systems. However, while there has been significant advances in developing these systems, ...

Over the years, mathematical models have become increasingly complex. Rarely can we accurately model a process using only linear or quadratic functions. Instead, we must employ complicated routines written in some programming ...

Optimal control problems for partial differential equations of evolution, mostly of parabolic type, are considered. The means of control are a nonhomogeneous boundary condition or forcing term.
A hierarchical control problem ...

The determination of first-arrival seismic traveltimes radiating outward from a point-source in an arbitrary slowness field plays an important role in methods which require knowledge of curved wavefronts in a complex domain. ...

In this thesis, we develop an efficient accurate numerical algorithm for evaluating a few of the smallest eigenvalues and their corresponding eigenvectors for large scale nonlinear eigenproblems. The entries of the matrices ...

Real Earth media are anelastic, which affects both the kinematics and dynamics of propagating waves: Waves are attenuated and dispersed. If anelastic effects are neglected, inversion and migration can yield erroneous ...

The Arnoldi algorithm, or iteration, is a computationally attractive technique for computing a few eigenvalues and associated invariant subspace of large, often sparse, matrices. The method is a generalization of the Lanczos ...

Two classes of primal-dual interior-point methods for nonlinear programming are studied. The first class corresponds to a path-following Newton method formulated in terms of the nonnegative variables rather than all primal ...